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View new features for Radioss 2024.
Overview
Radioss^® is a leading explicit finite element solver for crash and impact simulation.
Tutorials
Discover Radioss functionality with interactive tutorials.
User Guide
This manual provides details on the features, functionality, and simulation methods available in Altair Radioss.
Reference Guide
This manual provides a detailed list of all the input keywords and options available in Radioss.
Example Guide
This manual presents examples solved using Radioss with regard to common problem types.
Verification Problems
This manual presents solved verification models.
Frequently Asked Questions
This section provides quick responses to typical and frequently asked questions regarding Radioss.
Theory Manual
This manual provides detailed information about the theory used in the Altair Radioss Solver.
- Large Displacement Finite Element Analysis Theory Manual
- ALE, CFD and SPH Theory Manual
  - ALE Formulation
    ALE or Arbitrary Lagrangian Eulerian formulation is used to model the interaction between fluids and solids; in particular, the fluid loading on structures. It can also be used to model fluid-like behavior, as seen in plastic deformation of materials.
  - Computational Aero-Acoustic
  - Smooth Particle Hydrodynamics
    Smooth Particle Hydrodynamics (SPH) is a meshless numerical method based on interpolation theory. It allows any function to be expressed in terms of its values at a set of disordered point's so-called particles.
    - SPH Approximation of a Function
    - Corrected SPH Approximation of a Function
    - SPH Integration of Continuum Equations
    - Artificial Viscosity
    - Time Step Control Stability
      The stability conditions of explicit scheme in SPH formulation can be written over cells or on nodes.
    - Conservative Smoothing of Velocities
    - SPH Cell Distribution
- Appendix A: Basic Relations of Elasticity
User Subroutines
This manual describes the interface between Altair Radioss and user subroutines.

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Artificial Viscosity

As usual in SPH ^¹ implementations, viscosity is rather an inter-particles pressure than a bulk pressure. It was shown that the use of Equation 1 and Equation 2 generates a substantial amount of entropy in regions of strong shear even if there is no compression.

$π_{i j} = \frac{- q_{b} \frac{c_{i} + c_{j}}{2} μ_{i j} + q_{α} μ_{i j}^{2}}{\frac{(ρ_{i} + ρ_{j})}{2}}$

with

$μ_{i j} = \frac{d_{i j} (v_{i} - v_{j}) • (X_{i} - X_{j})}{{‖ X_{i} - X_{j} ‖}^{2} + ε d_{i j}^{2}}$

Where, $X_{i}$ (resp. $X_{j}$ ) indicates the position of particle I (resp. $j$ ) and $c_{i}$ (resp $c_{j}$ ) is the sound speed at location $i$ (resp. $j$ ), and $q_{a}$ and $q_{b}$ are constants. This leads us to introduce Equation 3 and Equation 4. ^² The artificial viscosity is decreased in regions where vorticity is high with respect to velocity divergence.

$π_{i j} = \frac{- q_{b} \frac{c_{i} + c_{j}}{2} μ_{i j} + q_{α} μ_{i j}^{2}}{\frac{(ρ_{i} + ρ_{j})}{2}}$

with

$μ_{i j} = \frac{d_{i j} (v_{i} - v_{j}) • (X_{i} - X_{j})}{{‖ X_{i} - X_{j} ‖}^{2} + ε d_{i j}^{2}} \frac{(f_{i} + f_{j})}{2}, f_{k} = \frac{‖ {\nabla \cdot v |}_{k} ‖}{‖ {\nabla \cdot v |}_{k} ‖ + ‖ {\nabla \times v |}_{k} ‖ + ε^{'} \frac{c_{k}}{d_{k}}}$

Default values for $q_{a}$ and $q_{b}$ are respectively set to 2 and 1.

Monaghan J.J., Smoothed Particle Hydrodynamics, Annu.Rev.Astron.Astro-phys; Vol. 30; pp. 543-574, 1992.

Balsara D.S., Von Neumann Stability Analysis of Smoothed Particle Hydrodynamics Suggestions for Optimal Algorithms, Journal of Computational Physics, Vol. 121, pp. 357-372, 1995.